Law(s) of Large Numbers
It is a well-known fact that averages of most random variables converge. The laws of large numbers are mathematical theorems which explain this phenomenon. We discuss the various forms of this theorem. Generalizations to dependent variables (ergodic ths) are introduced. We also mention uniform laws of large numbers, which are quite indispensable tools to prove consistency of estimators.
KeywordsBernoulli experiments Bernoulli, J. Ergodic theorems Law of large numbers Maximum likelihood Poisson, S. D. Probability Strong law of large numbers Variance Weak law of large numbers
- Billingsley, P. 1995. Probability and measure. 3rd ed. New York: Wiley.Google Scholar
- Gray, R.M. 2007. Probability, random processes, and ergodic properties. Online. Available at http://ee.stanford.edu/Bgray/arp.html. Accessed 29 Apr 2007.
- Hall, P., and C.C. Heyde. 1980. Martingale limit theory and its application. San Diego: Academic Press.Google Scholar
- Hayashi, F. 2000. Econometrics. Princeton: Princeton University Press.Google Scholar